# Connections in a state

Discrete Mathematics Level pending

A certain fictional state has 12 cities in it, each with railroads emanating from them. The cities have (in no particular order) $1,1,2,2,3,3,4,4,4,5,8,9$ Railroads emanating from them. Define a Connection to be a path from $$A$$ to $$B$$ through a certain city $$C$$. $$A$$ and $$B$$ do not have to be distinct (i.e. sightseers going to a city then returning), though $$A \rightarrow C \rightarrow B$$ is distinct from $$B \rightarrow C \rightarrow A$$. Find the number of possible connections in this state.

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